Feb 27 2012
Two group difference of means test:
A lot of people in Canada compared to are neither believers nor non-
Non-believer and believer: do these two groups have the same or
different levels of distress?
• Imagining another table that has believers and their level of
distress (mean) and compare it to non-believers, we should be
able to see if the relaxed got hypothesis is true, then believers
should have lower distress.
• Null hypothesis, in the sample of which this population was drawn,
there is no difference in mean level of distress
• Operationalization of distress: The distress index that is used in
the research analysis paper
Cases drop off - people who didn't answer the distress items are not in
People forget that this is all estimates. Nothing is precise. Thing to keep
in mind is comparison and estimate.
• Look for example to refute null hypothesis
• Two tail test means, rather than suggesting a direction, let's just
say there is a difference. it could be this way, or it could be the
• Means are just one part of the story. another part of the story is
• Ideal is, you want believers and non believers to be far apart. You
don't want a lot of spread between groups. if u ave believers here
and non believers in other side in an index, far apart and
Imagine that at some point u have to almost hypothetically, sample
after sample, scooping up if null hypothesis is true, if its close to zero,
just plot it on frequency distribution.
Just like the dice example in the book, if you scoop up a population and
it gives you a big difference, something is wrong, or null hypothesis is
It's like taking that dice example and pulling that to the example prof
Feb 27 2012
SOC202 Quantitative Analysis in Social Sciences
SP.TG. Page 2
gave. How likely is it get to 2 or a 12 rolling 2 dice? Very little.
Ideal: bigger difference between means.
Believers have a bit, but not much. But it'll be statically significant
because the sample population is large.
Instead of getting 60 000, if we did a study of 500 canadians, these
kinds of SD will be hard to reach a statically significant effect.
In larger samples, gives you a more flexibility to have larger variation.
Versus smaller samples, there are greater fluctuations around the
Prof wants to be able to talk about the bigger difference between the
means (eg. this group is different from the other group, and there is
small variance etc (you want SD to be somewhat similar))
T-statistic: here's the centre, t-statisitic that you would get if null
hypothesis is true, is zero. You're building a case against the null
The numerator (test effect) in the case against the null is the difference
between the two means.
Denominator is the standard error. It is the pooled variance estimate.
Sample to sample to sample variability is the pooled variance.
The whole idea here is, t-statistic is 'test error divided by standard error'
p-value the tee will set is .05. We'll say it is a two-tailed test (Believers
could be better off, or not better off).
Null hypothesis is in the middle.
On average, people who agree or strongly agree with the statement "the
challenges i face in lfe are god sway of testing me" report a higher level
of distress compared to study participants who reject or deny this
There is a real difference in the levels of distress b/w believe era and
* highly unlikely the that observed difference of .618 resulted from
normal, expected from sampling error. Statistically speaking, it is
different enough from expected, from giving a confide